Unitary matrices associated with Butson-Hadamard matrices
We give an example of a BH(5; 5) matrix M satisfying that the eigenvalues of the unitary matrix $\frac{1}{\sqrt5}M$ are all primitive 10-th roots of unity and such that $\frac{1}{5}M^3$ is not a BH(5; 5) matrix. This example gives a negative answer to a conjecture proposed by R. Egan and P. O. Cathain.
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Combinatorics
